Given that $f(x) = x^{2}-2x+5$ and $g(x) =x+3$, what is the value of $f(g(5)) -g(f(5))$?
Since $g(5) = 5+3=8$ and $f(5) = 5^2 - 2(5) + 5 = 25-10+5 = 20$, we have $f(g(5)) -g(f(5)) = f(8) - g(20) = 8^2 - 2(8) + 5 - (20+3) = 64 - 16 + 5 - 23 = \boxed{30}$.